A parallel plate capacitor is made up of stair like structure with a… | JEE Main 2022 (27 Jun, Shift 2)

Q59JEE Main 2022 · 27 JUN · SHIFT 2Difficult

Combination of Capacitors

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $\frac{x}{15}\frac{\epsilon_0 A}{b}$ . The value of x is ____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 23

Facing stairs of the two plates form three capacitors of area $A$ each, all joined by the plates, so they are in parallel.
Gaps: innermost pair $b$ , next pair $b + 2b = 3b$ , outer pair $3b + 2b = 5b$ .
$C = \frac{\epsilon_0 A}{b}\left(1 + \frac{1}{3} + \frac{1}{5}\right) = \frac{23}{15}\frac{\epsilon_0 A}{b}$
So $x = 23$ .

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